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The expansion of functions under transformation and its application to optimization. (English) Zbl 0847.73076
Summary: This paper proposes the expansion of functions under transformation, which represents infinite kinds of extensions of Taylor’s expansion. Based on this, Duffin’s condensation formula is developed as a condensation formula of high order. Furthermore, a theorem on efficiently solving mathematical programming by using the expansion of functions is proposed. According to the condensation formula of high order, two kinds of second order primal algorithms are proposed for solving generalized geometric programming with rapid and stable convergence, which could be applied to a wide range of structural optimization problems. Finally, an efficient fully stressed design method under the function transformation is proposed using these expansions of functions.

MSC:
74S30Other numerical methods in solid mechanics
74P99Optimization in solid mechanics
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References:
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[2] Rijckaert, M. J.; Martens, X. M.: Comparison of generalized geometric programming algorithms. Advances in geometric programming, 283-320 (1980) · Zbl 0444.49028
[3] Avriel, M.; Dembo, R. S.; Passy, U.: Solution of generalized geometric programming. Internat. J. Numer. methods engrg. 9, 149-168 (1975) · Zbl 0299.65035
[4] Morris, A. J.: Structural optimization by geometric programming. Internat. J. Solid structures 8, 847-864 (1972) · Zbl 0255.73086
[5] Ragsdell, K. M.; Phillips, D. T.: Optimal design of class of welded structurs using geometric programming. J. engrg. Ind., trans. ASME, series B 98, 1021-1025 (1976)